LeParmentier died on Tuesday morning in Austin while visiting his children, according to his publicist, Derek Maki, who said he does not know the cause of death.
The actor was born in Pittsburgh, but later moved to Britain in 1974 and had been living in Bath, England.
In 1997's "Star Wars," LeParmentier's character Death Star Admiral Motti mocks Vader's "sad devotion to that ancient Jedi religion." Vader responds with a demonstration, using the force to choke the young commander, but allowing him to live.
LeParmentier had many roles in British TV throughout his career and was working as a screenwriter when he died. He played a reporter in "Superman II" in 1980. The film featured actress Sarah Dougless - the villainess Ursa - with whom he was married from 1981 until 1984, according to their online movie profiles.
His part in "Star Wars" is likely the standout role in his career.
"He absolutely loved traveling the world and meeting his friends and fellow 'Stars Wars' fans, whose tributes have given us all the best lines in this message," LeParmentier's family said in a statement.
"He was no respecter of convention, except comic conventions," said Rhiannon, Stephanie and Tyrone LeParmentier.
"Every time we find someone's lack of faith disturbing, we'll think of him," they said.
The Associated Press contributed to this report.